How to carry out the tangents to circles

A tangent to a given circle is called a straight line that has only one common point with the circle. Tangent to a circle is always perpendicular to its radius drawn to the tangent point. If two tangents drawn from one point, not belonging to a circle, then the distance between this point and the touch points will always be the same. Tangents to circles are constructed in different ways, depending on their location relative to each other.

Instruction

1. The construction of the tangent to the same circle.
   1. Built a circle of radius R and take a point A, to go through the tangent.
   2. Construct the circle with center in the midpoint of the segment OA and the radius equal to half of this segment.
   3. The intersection of two circles are the points of tangency of tangents drawn through point A to a given circle.
   
2. External tangent to two circles.
   1. Built two circles of radius R and r.
   2. Is a circle of radius R – r centered at the point O.
   3. To the resulting circle is tangent from point O1, the point of tangency is marked with the letter M.
   4. The radius R passing through the point M indicates the point T – the point of tangency of a great circle.
   5. Through the center O1 of the small circle is of radius r parallel to the radius R of the large circle. The radius r indicates the point T1 to the point of tangency of the small circle.
   6. Video TT1 – tangent to the given circles.
   
3. Internal tangent to two circles.
   1. Built two circles of radius R and r.
   2. Is a circle of radius R + r centered at the point O.
   3. To the resulting circle is tangent from point O1, the point of tangency is marked with the letter M.
   4. OM the ray intersects the first circle at a point T in the tangent point of a great circle.
   5. Through the center O1 of the small circle is of radius r parallel to the ray OM. The radius r indicates the point T1 to the point of tangency of the small circle.
   6. Video TT1 – tangent to the given circles.